I
nd
o
ne
s
ia
n J
o
urna
l o
f
E
lect
rica
l En
g
ineering
a
nd
Co
m
pu
t
er
Science
Vo
l.
41
,
No
.
2
,
Feb
r
u
ar
y
20
2
6
,
p
p
.
456
~
469
I
SS
N:
2
502
-
4
7
52
,
DOI
: 1
0
.
1
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cs
.v
41
.
i
2
.
pp
456
-
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6
9
456
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Co
ntrol o
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C
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sy
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m
s
c
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p
a
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a
t
c
o
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li
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h
t
in
t
o
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lec
tri
c
a
l
e
n
e
rg
y
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i
n
terc
o
n
n
e
c
ted
d
irec
tl
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with
th
e
u
ti
li
t
y
g
r
id
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Th
e
se
sy
ste
m
s
c
o
m
p
rise
se
v
e
ra
l
k
e
y
c
o
m
p
o
n
e
n
ts:
P
V,
m
u
lt
il
e
v
e
l,
c
o
n
tr
o
ll
e
rs,
a
n
d
g
ri
d
in
terfa
c
e
e
q
u
ip
m
e
n
t
.
I
n
t
h
is
c
o
n
t
e
x
t,
fi
v
e
-
lev
e
l
in
v
e
rters
a
re
i
n
c
re
a
sin
g
ly
fa
v
o
u
re
d
o
v
e
r
th
re
e
-
lev
e
l
i
n
v
e
rt
e
rs
d
u
e
t
o
th
e
ir
a
b
il
it
y
t
o
re
d
u
c
e
t
o
tal
h
a
rm
o
n
ic
d
isto
rti
o
n
(
THD
)
,
imp
ro
v
e
e
fficie
n
c
y
,
a
n
d
e
n
su
re
b
e
tt
e
r
p
o
we
r
q
u
a
li
ty
i
n
g
rid
-
c
o
n
n
e
c
ted
a
p
p
li
c
a
ti
o
n
s.
Th
is
re
se
a
rc
h
p
re
se
n
ts
a
th
re
e
-
lev
e
l
e
n
h
a
n
c
e
d
c
o
n
tro
l
sc
h
e
m
e
a
ime
d
a
t
o
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ti
m
izin
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th
e
p
e
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rm
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n
c
e
o
f
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g
rid
-
c
o
n
n
e
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ted
p
h
o
to
v
o
l
taic
sy
ste
m
wit
h
a
fiv
e
-
lev
e
l
in
v
e
rter.
A
fra
c
ti
o
n
a
l
-
o
r
d
e
r
p
ro
p
o
rti
o
n
a
l
-
i
n
teg
ra
l
(F
OPI)
c
o
n
tro
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ler i
s
u
ti
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z
e
d
fo
r
m
a
x
imu
m
p
o
we
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p
o
in
t
t
ra
c
k
i
n
g
(M
P
P
T)
to
e
n
s
u
re
p
re
c
ise
trac
k
in
g
u
n
d
e
r
v
a
riab
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irrad
ia
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e
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o
n
d
it
io
n
s.
At
th
e
g
rid
-
i
n
terfa
c
e
sta
g
e
,
a
m
o
d
if
ied
a
c
ti
v
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d
istu
r
b
a
n
c
e
re
jec
ti
o
n
c
o
n
tr
o
ll
e
r
(
M
AD
RC)
is
d
e
v
e
lo
p
e
d
fo
r
g
rid
-
in
terfa
c
e
,
fe
a
tu
rin
g
a
n
in
n
e
r
lo
o
p
f
o
r
DC
-
l
in
k
v
o
l
tag
e
re
g
u
lati
o
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b
a
se
d
o
n
Ly
a
p
u
n
o
v
th
e
o
ry
,
lea
d
in
g
t
o
imp
ro
v
e
d
d
y
n
a
m
ic
p
e
rfo
rm
a
n
c
e
with
lo
we
r
THD
o
f
th
e
g
rid
c
u
rre
n
t
a
n
d
e
n
h
a
n
c
e
d
e
fficie
n
c
y
.
S
imu
lati
o
n
re
su
lt
s
h
ig
h
li
g
h
t
t
h
e
e
ffe
c
ti
v
e
n
e
ss
o
f
t
h
e
p
r
o
p
o
se
d
sy
ste
m
.
Co
m
p
a
re
d
wit
h
th
e
F
OPI
-
AD
RC,
a
th
re
e
-
lev
e
l
c
o
n
fig
u
ra
ti
o
n
(
0
.
3
8
%
THD),
th
e
p
r
o
p
o
se
d
F
OPI
-
M
AD
RC
with
a
fiv
e
-
lev
e
l
i
n
v
e
rter
a
c
h
iev
e
s
su
p
e
r
io
r
p
e
rfo
rm
a
n
c
e
,
wit
h
o
n
ly
(0
.
2
2
%
THD).
Th
e
se
re
su
lt
s
c
o
n
firm
th
e
a
d
v
a
n
tag
e
s
o
f
c
o
m
b
i
n
in
g
a
d
v
a
n
c
e
d
c
o
n
tr
o
l
stra
teg
ies
with
m
u
lt
il
e
v
e
l
in
v
e
rt
e
r
tec
h
n
o
lo
g
y
i
n
imp
ro
v
i
n
g
b
o
th
p
o
we
r
q
u
a
li
t
y
a
n
d
sy
ste
m
e
fficie
n
c
y
.
K
ey
w
o
r
d
s
:
Activ
e
d
is
tu
r
b
an
ce
r
ejec
tio
n
co
n
tr
o
ller
Gr
id
Mo
d
if
ied
ac
tiv
e
d
is
tu
r
b
an
ce
r
ejec
tio
n
co
n
tr
o
ller
Mu
ltil
ev
el
Neu
tr
al
p
o
in
t c
lam
p
e
d
in
v
er
te
r
Ph
o
to
v
o
ltaic
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Gh
er
ici
Din
ar
L
STE
L
ab
o
r
ato
r
y
o
f
E
n
v
ir
o
n
m
en
tal
Scien
ce
an
d
T
ec
h
n
o
l
o
g
y
,
Un
iv
e
r
s
ity
Mu
s
tap
h
a
Stam
b
o
u
li o
f
Ma
s
ca
r
a
Ma
s
ca
r
a,
Alg
er
ia
E
m
ail:
d
n
r
.
g
h
r
c
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
E
n
er
g
y
p
r
o
d
u
ctio
n
is
a
m
ajo
r
ch
allen
g
e
f
o
r
th
e
c
o
m
in
g
y
ea
r
s
[
1
]
.
I
n
d
ee
d
,
t
h
e
e
n
er
g
y
n
ee
d
s
o
f
in
d
u
s
tr
ialized
s
o
cieties
co
n
tin
u
e
to
in
c
r
ea
s
e.
So
lar
e
n
er
g
y
s
y
s
tem
s
p
r
o
d
u
ctio
n
is
a
m
ajo
r
ch
allen
g
e
f
o
r
th
e
co
m
in
g
y
ea
r
s
,
as
th
ey
ar
e
e
f
f
icien
t
in
g
en
er
atin
g
elec
tr
ici
ty
in
a
clea
n
m
an
n
er
.
So
lar
en
er
g
y
is
th
e
m
o
s
t
p
r
o
m
is
in
g
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
,
an
d
p
h
o
t
o
v
o
ltaic
(
PV
)
p
o
wer
g
e
n
er
atio
n
h
as
b
ec
o
m
e
o
n
e
o
f
th
e
m
o
s
t
u
s
ed
r
en
ewa
b
le
en
er
g
y
p
o
wer
g
en
er
atio
n
m
eth
o
d
s
[
2
]
,
[
3
]
.
T
h
e
d
ev
elo
p
m
en
t
an
d
u
tili
za
tio
n
o
f
PV
p
o
wer
g
en
er
atio
n
tec
h
n
o
lo
g
y
h
as r
ec
eiv
ed
wid
esp
r
ea
d
atten
tio
n
in
co
u
n
tr
ies all
o
v
er
th
e
wo
r
l
d
[
4
]
,
[
5
]
.
PV
is
a
p
r
o
ce
s
s
o
f
co
n
v
er
tin
g
lig
h
t
en
er
g
y
i
n
to
elec
tr
ical
en
er
g
y
[
6
]
,
[
7
]
.
PV
p
o
wer
g
en
er
atio
n
h
as
th
e
ad
v
an
tag
e
o
f
en
v
ir
o
n
m
e
n
tal
f
ac
to
r
s
an
d
h
as
r
an
d
o
m
n
ess
an
d
v
o
latilit
y
.
R
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
esp
ec
ially
PV
o
n
es,
ar
e
b
ec
o
m
in
g
m
o
r
e
an
d
m
o
r
e
in
ter
e
s
tin
g
d
u
e
to
t
h
e
p
r
ed
icted
lack
o
f
c
o
n
v
e
n
tio
n
al
s
o
u
r
ce
s
o
v
er
th
e
co
m
in
g
y
ea
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
C
o
n
tr
o
l o
f m
u
lti
-
leve
l NPC
in
ve
r
ters
in
P
V
/g
r
id
s
y
s
tems u
s
i
n
g
A
DR
C
a
n
d
MADR
C
(
Gh
erici Din
a
r
)
457
T
h
e
PV
g
r
id
-
co
n
n
ec
ted
in
v
e
r
t
er
is
an
im
p
o
r
tan
t
p
o
wer
elec
t
r
o
n
ic
c
o
n
v
e
r
ter
t
o
r
ea
lize
d
ir
e
ct
cu
r
r
e
n
t
-
alter
n
atin
g
c
u
r
r
en
t
(
DC
-
AC
)
co
n
v
er
s
io
n
.
T
h
e
PV
g
r
id
-
c
o
n
n
ec
ted
in
v
e
r
ter
is
th
e
in
t
er
f
ac
e
b
et
wee
n
th
e
r
en
ewa
b
le
en
er
g
y
p
o
we
r
g
en
e
r
atio
n
s
y
s
tem
s
an
d
th
e
p
o
wer
g
r
id
,
an
d
it p
lay
s
a
d
ec
is
iv
e
r
o
le
in
g
r
id
-
co
n
n
ec
ted
p
o
wer
g
en
er
atio
n
.
T
h
e
ass
o
ci
atio
n
o
f
th
e
PV
s
tatio
n
co
n
n
ec
ted
to
t
h
e
elec
tr
icity
n
etwo
r
k
is
d
o
n
e
u
s
in
g
a
co
n
tin
u
o
u
s
/alter
n
ate
cu
r
r
e
n
t c
o
n
v
er
ter
.
Gen
er
ally
,
in
th
e
liter
atu
r
e,
we
n
o
te
th
at
th
e
wo
r
k
d
ea
ls
with
th
e
co
n
tr
o
l
o
f
s
im
p
le
class
i
c
in
v
er
ter
s
an
d
ev
en
th
o
s
e
tr
ea
ted
b
y
m
u
lt
ilev
el
in
v
er
ter
s
h
av
e
b
ee
n
lim
i
ted
to
th
e
class
ic
m
ax
im
u
m
p
o
wer
p
o
in
t tr
ac
k
in
g
(
MPPT)
co
n
tr
o
l
o
f
th
e
ch
o
p
p
er
th
at
is
u
p
s
tr
ea
m
o
f
th
e
in
v
e
r
ter
.
I
t
is
also
n
o
ted
t
h
at
th
er
e
is
litt
le
wo
r
k
d
o
n
e
o
n
n
o
n
lin
ea
r
c
o
n
tr
o
l
o
f
m
u
ltil
ev
el
n
eu
tr
al
p
o
i
n
t
clam
p
ed
(
NPC
)
in
v
er
ter
s
,
o
r
th
at
th
e
wo
r
k
is
lim
ited
to
co
n
d
u
ctin
g
s
im
u
latio
n
s
o
r
ca
r
r
y
in
g
o
u
t e
x
p
e
r
im
en
ts
f
o
r
o
n
e
t
y
p
e
o
f
in
v
er
ter
with
o
u
t c
o
m
p
a
r
is
o
n
s
o
r
test
in
g
o
f
p
ar
am
eter
ch
an
g
es
[
8
]
.
Du
r
in
g
th
e
r
esear
ch
,
n
o
c
o
m
p
ar
is
o
n
was
m
ad
e
with
a
n
o
th
er
tech
n
o
lo
g
y
o
r
ev
e
n
with
an
in
v
er
ter
o
f
a
n
o
th
er
ty
p
e.
T
h
is
r
esear
ch
will
m
ain
ly
f
o
cu
s
o
n
co
n
tr
o
llin
g
th
e
g
r
id
-
s
id
e
in
v
er
ter
in
o
r
d
er
to
r
ed
u
ce
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
co
n
ten
t.
T
h
e
wo
r
k
aim
s
to
co
m
p
ar
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
a
th
r
ee
-
lev
el
an
d
a
f
iv
e
-
lev
el
NPC
co
n
v
er
ter
u
s
ed
in
a
PV g
en
er
atio
n
s
y
s
tem
co
n
n
ec
ted
to
a
n
o
n
lin
ea
r
elec
tr
ic
al
n
etwo
r
k
.
T
h
e
ADRC
co
n
tr
o
l stra
teg
y
is
b
ased
o
n
th
e
e
x
ten
d
e
d
s
tate
o
b
s
er
v
er
(
E
SO)
,
wh
ich
c
o
n
s
titu
tes its
co
r
e
an
d
allo
ws esti
m
atio
n
an
d
ca
n
ce
llatio
n
o
f
v
ar
io
u
s
ex
ter
n
al
an
d
in
ter
n
al
d
is
tu
r
b
a
n
ce
s
o
f
th
e
s
y
s
tem
in
r
ea
l tim
e
[
9
]
.
T
h
is
o
b
s
er
v
er
h
as
th
e
ad
v
an
tag
e
th
at
it
d
o
es
n
o
t
r
eq
u
ir
e
co
m
p
lete
k
n
o
wled
g
e
an
d
ex
a
ct
s
y
s
tem
co
n
tr
o
l.
Fu
r
th
er
m
o
r
e
,
it a
llo
ws f
o
r
r
e
d
u
cin
g
th
e
tim
e
r
eq
u
ir
e
d
to
esta
b
lis
h
a
d
etailed
m
o
d
el
o
f
th
e
s
tu
d
ied
s
y
s
tem
.
T
h
e
m
o
d
if
ied
ac
tiv
e
d
is
tu
r
b
an
ce
r
ejec
tio
n
co
n
tr
o
l
(
MA
DR
C
)
r
ef
er
s
to
v
ar
io
u
s
alter
atio
n
s
o
r
en
h
an
ce
m
e
n
ts
m
ad
e
to
th
e
s
ta
n
d
ar
d
ADRC
d
esig
n
to
im
p
r
o
v
e
its
p
er
f
o
r
m
an
ce
,
ad
d
r
ess
s
p
ec
if
ic
ch
allen
g
es,
o
r
s
im
p
lify
im
p
lem
en
tatio
n
.
T
h
e
s
e
m
o
d
if
icatio
n
s
o
f
ten
i
n
v
o
lv
e
ch
an
g
es
to
th
e
E
SO
o
r
th
e
f
e
ed
b
ac
k
c
o
n
tr
o
l
law
.
T
h
e
r
esear
ch
will
also
p
r
o
v
id
e
a
co
m
p
ar
is
o
n
b
etwe
en
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
ADRC
an
d
MA
DR
C
co
n
tr
o
lle
r
s
in
r
eg
u
latin
g
AC
g
r
id
s
.
Pen
d
in
g
t
h
e
wo
r
k
,
PQ th
eo
r
y
was u
s
ed
t
o
d
eter
m
in
e
h
ar
m
o
n
ic
cu
r
r
en
ts
.
T
h
e
s
tu
d
y
[
1
0
]
a
n
aly
z
ed
a
g
r
id
-
tied
PV
s
y
s
tem
,
s
u
g
g
esti
n
g
a
co
n
tr
o
l
m
eth
o
d
f
o
r
th
e
g
r
id
-
s
id
e
co
n
v
er
ter
(
GSC
)
u
s
in
g
a
th
r
ee
-
lev
el
d
io
d
e
-
clam
p
ed
m
u
l
tilev
el
in
v
er
t
er
with
v
o
ltag
e
-
o
r
ien
tated
co
n
t
r
o
l
(
VOC).
T
h
e
p
er
f
o
r
m
a
n
ce
was
as
s
ess
ed
b
ased
o
n
in
v
er
ter
an
d
g
r
id
cu
r
r
e
n
t
an
d
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
b
u
t
d
id
n
o
t
ev
al
u
ate
th
e
PV
s
y
s
tem
's
ef
f
icien
cy
.
Ali
et
a
l.
[
1
1
]
d
escr
ib
ed
a
g
r
i
d
-
tied
PV
s
y
s
tem
u
s
in
g
th
e
p
er
tu
r
b
atio
n
an
d
o
b
s
er
v
at
io
n
(
P&
O)
MPPT
alg
o
r
ith
m
,
with
m
o
d
el
p
r
ed
ictiv
e
c
o
n
tr
o
l
(
MPC
)
m
an
ag
in
g
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
.
R
esu
lts
s
h
o
wed
th
e
MPC
ef
f
ec
tiv
el
y
co
n
n
ec
ted
th
e
s
o
lar
s
y
s
tem
t
o
th
e
g
r
id
wh
ile
t
h
e
MPPT
tr
ac
k
ed
m
ax
im
u
m
p
o
wer
.
A
d
if
f
er
en
t
s
tu
d
y
[
1
2
]
f
o
cu
s
ed
o
n
s
im
u
latin
g
a
g
r
id
-
co
n
n
ec
ted
PV
s
y
s
tem
with
a
th
r
ee
-
p
h
ase
in
v
er
ter
a
n
d
a
b
o
o
s
t
co
n
v
er
ter
.
I
t
i
n
tr
o
d
u
ce
d
a
n
ad
v
a
n
ce
d
MPPT
co
n
tr
o
ller
u
s
in
g
lin
ea
r
m
atr
ix
in
e
q
u
ality
(
L
MI
)
to
im
p
r
o
v
e
ef
f
icien
c
y
a
n
d
r
ed
u
ce
c
u
r
r
en
t
T
HD.
I
t
co
m
p
ar
ed
m
u
lt
i
-
lev
el
in
v
er
te
r
s
an
d
co
n
tr
o
l
tec
h
n
iq
u
es,
f
in
d
i
n
g
t
h
e
th
r
ee
-
le
v
el
NPC
in
v
er
ter
with
in
teg
r
al
b
ac
k
s
tep
p
in
g
c
o
n
tr
o
l
s
u
p
er
io
r
.
T
h
e
ac
tiv
e
d
is
tu
r
b
an
ce
r
ejec
tio
n
c
o
n
tr
o
ller
(
ADRC
)
an
d
im
p
r
o
v
ed
MA
DR
C
wer
e
p
r
o
p
o
s
ed
p
o
u
r
u
n
e
meilleu
r
e
s
ta
b
ilit
é
et
r
ésil
ien
ce
d
a
n
s
d
ivers
es
co
n
d
itio
n
s
.
T
h
e
r
esea
r
ch
h
ig
h
lig
h
ts
th
e
n
ee
d
f
o
r
o
p
tim
izin
g
co
n
tr
o
l
s
y
s
tem
s
f
o
r
g
r
id
-
c
o
n
n
ec
ted
PV p
o
wer
s
y
s
tem
s
.
T
o
im
p
r
o
v
e
p
o
wer
q
u
ality
in
th
e
g
r
id
an
d
e
n
h
an
ce
en
er
g
y
ex
tr
ac
tio
n
f
r
o
m
s
o
lar
p
an
els,
in
tellig
en
t
n
o
n
lin
ea
r
c
o
n
tr
o
l
s
y
s
tem
s
ar
e
n
ee
d
ed
.
T
h
is
p
ap
e
r
s
u
g
g
ests
a
n
ew
m
eth
o
d
th
at
co
m
b
in
es
a
MA
DR
C
f
o
r
g
r
id
r
eg
u
latio
n
with
f
r
ac
tio
n
al
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
FOPI)
co
n
tr
o
ller
s
f
o
r
MPPT.
T
h
e
g
o
a
l
is
to
en
h
an
ce
th
e
p
er
f
o
r
m
an
ce
o
f
f
iv
e
-
lev
el
in
v
e
r
ter
-
b
ased
PV sy
s
tem
s
.
T
h
is
p
ap
er
h
as b
ee
n
o
r
g
an
ize
d
in
f
o
u
r
s
ec
tio
n
s
,
wh
er
e
t
h
e
f
ir
s
t
s
ec
tio
n
was
th
e
p
ap
er
in
tr
o
d
u
ctio
n
.
I
n
th
e
s
ec
o
n
d
s
ec
tio
n
,
we
ar
e
in
te
r
ested
in
th
e
m
o
d
ellin
g
o
f
th
e
en
tire
PV
s
y
s
tem
co
m
p
o
n
en
t,
g
o
in
g
f
r
o
m
t
h
e
PV
ce
ll
to
th
e
co
n
n
ec
tio
n
with
th
e
u
tili
ty
g
r
id
.
T
h
e
th
ir
d
s
ec
tio
n
was
d
e
v
o
te
d
to
t
h
e
m
ath
em
atica
l
m
o
d
el
o
f
th
e
ADR
C
an
d
MA
DR
C
.
T
h
e
s
i
m
u
latio
n
r
esu
lts
o
f
th
e
th
r
ee
-
p
h
ase
g
r
id
-
c
o
n
n
ec
ted
PV
s
y
s
t
em
ar
e
p
r
esen
ted
in
th
e
f
o
u
r
th
s
ec
tio
n
.
2.
M
E
T
H
O
D
2
.
1
.
Sy
s
t
e
m
des
cr
iptio
n
I
n
th
is
s
ec
tio
n
we
ar
e
in
ter
ested
in
th
e
m
o
d
ellin
g
o
f
th
e
e
n
tir
e
PV
s
y
s
tem
co
m
p
o
n
e
n
t
g
o
in
g
f
r
o
m
th
e
PV
ce
ll
to
th
e
co
n
n
ec
tio
n
wit
h
th
e
u
tili
ty
g
r
id
.
T
h
e
s
tu
d
ied
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
1
,
an
d
it
co
n
s
is
ts
o
f
i)
a
PV
p
a
n
el
s
y
s
tem
,
ii)
a
DC
-
DC
b
o
o
s
t
co
n
v
er
te
r
an
d
M
PP
T
co
n
tr
o
l,
a
n
d
iii)
a
th
r
ee
-
an
d
f
i
v
e
-
lev
el
ty
p
e
NPC
in
v
er
ter
co
n
n
ec
ted
t
o
th
e
g
r
id
.
2
.
2
.
P
V
ce
ll
m
o
delin
g
T
o
ex
p
lain
th
e
m
o
d
ellin
g
o
f
a
PV
ar
r
ay
,
an
e
q
u
iv
alen
t
elec
tr
ical
cir
cu
it
o
f
th
e
s
am
e
is
s
h
o
wn
in
Fig
u
r
e
2
.
W
h
ich
co
n
s
is
ts
o
f
a
cu
r
r
e
n
t
s
o
u
r
ce
a
n
d
a
d
io
d
e
with
a
s
er
ies
an
d
p
ar
allel
r
esi
s
to
r
[
1
3
]
-
[
1
5
]
.
T
h
e
ch
ar
ac
ter
is
tic
eq
u
atio
n
is
g
iv
e
n
as f
o
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
41
,
No
.
2
,
Feb
r
u
a
r
y
20
2
6
:
4
5
6
-
4
6
9
458
−
−
−
=
0
(
1
)
w
h
er
e,
PV a
r
r
ay
c
u
r
r
e
n
t I
pv
ca
n
b
e
p
r
esen
ted
as,
=
−
−
(
2
)
R
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t
o
f
t
h
e
d
io
d
e
ca
n
b
e
g
iv
en
,
=
+
[
(
)
−
1
]
(
3
)
Mo
d
u
le
s
atu
r
atio
n
c
u
r
r
e
n
t I
0
c
an
b
e
s
h
o
wn
as,
=
[
(
)
3
∗
(
1
−
1
)
]
(
4
)
Fin
ally
,
PV c
u
r
r
en
t e
q
u
iv
alen
t
m
o
d
el
s
h
o
wn
in
F
ig
u
r
e
2
eq
u
atio
n
is
g
iv
en
as,
=
−
[
+
−
1
]
+
(
5
)
W
h
er
e,
I
p
v
=
c
ur
r
e
n
t
o
f
PV
m
o
d
el,
Id
=
d
io
d
e
cu
r
r
e
n
t,
I
s
c
=
s
h
o
r
t
cir
cu
it
cu
r
r
en
t,
Vd
=
v
o
ltag
e
ac
r
o
s
s
d
io
d
e,
Rp
=
r
esi
s
tan
ce
in
p
ar
allel,
Rs
=
s
er
ies
r
esi
s
tan
ce
,
Vo
c
=
o
p
en
cir
cu
it
v
o
ltag
e,
Ns
=
n
u
m
b
e
r
o
f
s
er
ies
s
tr
in
g
s
,
K=
B
o
ltzm
an
n
c
o
n
s
tan
t,
T
=
ab
s
o
lu
te
tem
p
er
atu
r
e
in
Kelv
in
.
Fig
u
r
e
1
.
T
h
r
ee
p
h
ase
g
r
id
c
o
n
n
ec
ted
PV sy
s
tem
Fig
u
r
e
2
.
E
q
u
iv
alen
t
m
o
d
el
o
f
s
in
g
le
d
io
d
e
s
o
lar
ce
ll
2
.
3
.
DC
-
DC
B
o
o
s
t
co
nv
er
t
er
a
nd
M
P
P
T
co
ntr
o
l
A
b
o
o
s
t
co
n
v
er
ter
in
cr
ea
s
es
th
e
v
alu
e
o
f
th
e
in
p
u
t
DC
v
o
ltag
e
to
th
e
n
ec
ess
ar
y
o
u
tp
u
t
v
o
ltag
e
lev
el
b
ec
au
s
e
th
e
DC
o
u
tp
u
t
v
o
lt
ag
e
o
f
t
h
e
PV
m
o
d
u
le
h
as
a
lo
w
v
alu
e
t
h
at
n
ee
d
s
to
b
e
co
n
v
e
r
ted
to
AC
co
m
p
atib
le
with
th
e
g
r
id
v
o
lt
ag
e
an
d
f
r
eq
u
en
cy
.
A
b
o
o
s
t
co
n
v
er
ter
i
s
also
k
n
o
wn
as
a
s
tep
-
u
p
co
n
v
er
ter
b
ec
au
s
e
it
u
s
es
an
in
d
u
cto
r
,
a
d
io
d
e,
a
ca
p
ac
ito
r
an
d
a
h
i
g
h
-
f
r
eq
u
e
n
cy
s
em
ico
n
d
u
cto
r
s
witch
to
o
p
er
ate
[
1
6
]
-
[
1
8
]
.
A
DC
/DC
b
o
o
s
t
co
n
v
er
ter
is
u
s
ed
a
s
a
co
n
tr
o
l
d
ev
ice
d
u
e
to
th
e
wid
e
u
tili
za
tio
n
o
f
s
u
ch
a
s
tep
-
up
DC
/D
C
st
r
u
ctu
r
e
in
PV sy
s
te
m
s
.
Fig
u
r
e
3
s
h
o
ws th
e
c
o
r
r
es
p
o
n
d
in
g
b
lo
ck
o
f
a
b
o
o
s
t c
o
n
v
er
ter
with
lo
ad
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
C
o
n
tr
o
l o
f m
u
lti
-
leve
l NPC
in
ve
r
ters
in
P
V
/g
r
id
s
y
s
tems u
s
i
n
g
A
DR
C
a
n
d
MADR
C
(
Gh
erici Din
a
r
)
459
=
−
(
1
−
)
+
1
(
6
)
=
(
1
−
)
−
1
(
7
)
W
h
er
e
Vin
=
in
p
u
t v
o
ltag
e,
Vo
u
t
=
o
u
tp
u
t v
o
ltag
e,
an
d
D
=
d
u
t
y
cy
cle
.
Du
e
to
th
eir
ab
ilit
y
to
s
y
n
th
esize
an
o
u
tp
u
t
v
o
ltag
e
g
r
ea
ter
t
h
an
th
e
v
o
ltag
e
r
atin
g
o
f
ea
c
h
s
witch
in
g
d
ev
ice,
m
u
ltil
ev
el
in
v
er
ter
s
h
a
v
e
s
ev
er
al
b
en
e
f
its
f
o
r
m
e
d
iu
m
-
an
d
h
ig
h
-
p
o
wer
s
y
s
tem
s
[
1
9
]
,
[
2
0
]
.
Fig
u
r
e3
.
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
m
o
d
el
MPPT
is
ap
p
lied
in
th
e
s
y
s
te
m
to
tr
ac
k
m
ax
im
u
m
p
o
wer
o
u
tp
u
t
f
r
o
m
s
o
lar
PV.
I
n
o
u
r
wo
r
k
,
b
y
co
m
b
in
in
g
MPPT
with
f
r
ac
ti
o
n
al
o
r
d
er
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
-
d
er
iv
ativ
e
(
FOPID
)
,
we
ac
h
iev
e
m
o
r
e
p
r
ec
is
e
an
d
r
esp
o
n
s
iv
e
c
o
n
tr
o
l
o
f
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
i
n
g
,
ev
e
n
u
n
d
er
v
a
r
iab
le
co
n
d
iti
o
n
s
s
u
ch
as
s
h
ad
in
g
o
r
ch
an
g
in
g
tem
p
er
atu
r
e
.
F
O
PID
co
n
tr
o
ller
s
(
μ
)
ar
e
t
h
e
c
o
n
tin
u
atio
n
o
f
c
o
n
v
e
n
tio
n
al
P
I
D
co
n
tr
o
l,
a
n
d
th
ey
ar
e
p
o
s
it
iv
e
r
ea
l
n
u
m
b
er
s
.
Fro
m
th
e
liter
atu
r
e,
o
n
e
ca
n
also
o
b
s
er
v
e
th
at
th
e
FOPID
co
n
tr
o
ller
en
h
an
ce
s
th
e
s
y
s
tem
p
er
f
o
r
m
an
ce
,
is
less
s
en
s
itiv
e
t
o
ch
an
g
es o
f
p
a
r
am
eter
s
an
d
a
ttain
s
th
e
p
r
o
p
er
t
y
o
f
is
o
-
d
am
p
in
g
v
e
r
y
ea
s
ily
.
T
h
e
g
en
e
r
al
f
o
r
m
o
f
t
h
e
FOPID
co
n
tr
o
ller
is
d
ef
i
n
ed
as [
2
1
]
.
(
)
=
(
)
(
)
=
+
+
(
,
≥
0
)
(
8
)
W
h
er
e
C
(
s
)
is
th
e
tr
an
s
f
er
f
u
n
ctio
n
m
o
d
el
o
f
t
h
e
FOPID
c
o
n
tr
o
ller
,
E
(
s
)
is
a
n
er
r
o
r
s
ig
n
al,
an
d
U(
s
)
is
th
e
co
n
tr
o
ller
’
s
o
u
tp
u
t,
a
n
d
th
e
b
l
o
ck
d
iag
r
am
o
f
th
e
FOPID
co
n
tr
o
ller
is
p
r
esen
ted
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
B
lo
ck
d
iag
r
am
FOPI
D
co
n
tr
o
ller
T
h
e
co
n
tr
o
l
s
ig
n
al
u
(
t)
is
s
tate
d
in
th
e
tim
e
d
o
m
ain
as
,
(
)
=
+
−
e(
t)
+
e(
t)
(
9
)
FOPID
-
b
ased
MPPT
o
f
f
er
s
s
i
g
n
if
ican
t
ad
v
a
n
tag
es
in
d
y
n
a
m
ic
p
er
f
o
r
m
an
ce
an
d
r
o
b
u
s
tn
ess
f
o
r
s
o
lar
s
y
s
tem
s
b
u
t
d
em
an
d
s
ca
r
ef
u
l
tu
n
in
g
an
d
ad
v
an
ce
d
h
ar
d
war
e.
I
t
b
r
id
g
es
th
e
g
ap
b
etwe
en
tr
ad
itio
n
al
PID
an
d
AI
-
b
ased
m
eth
o
d
s
,
m
ak
i
n
g
i
t
id
ea
l
f
o
r
ap
p
licatio
n
s
wh
er
e
ef
f
icien
cy
an
d
s
tab
ilit
y
ar
e
p
ar
am
o
u
n
t.
Fo
r
p
r
ac
tical
im
p
lem
en
tatio
n
,
s
tar
t w
ith
s
im
u
latio
n
s
(
MA
T
L
AB
)
an
d
u
s
e
m
etah
e
u
r
is
tics
f
o
r
o
p
ti
m
izatio
n
.
3.
M
UL
T
I
-
L
E
VE
L
CO
NV
E
R
T
E
R
S F
O
R
RE
N
E
WA
B
L
E
E
NE
RG
Y
SYS
T
E
M
S
Mu
ltil
ev
el
co
n
v
e
r
ter
s
ar
e
wid
ely
u
s
ed
in
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
to
im
p
r
o
v
e
p
o
w
er
q
u
ality
,
in
cr
ea
s
e
ef
f
icien
c
y
,
a
n
d
f
ac
ilit
ate
g
r
id
in
teg
r
atio
n
.
T
h
ey
ar
e
p
ar
ticu
lar
ly
b
en
ef
icial
f
o
r
ap
p
licatio
n
s
lik
e
win
d
en
er
g
y
s
y
s
tem
s
(
W
E
C
S)
an
d
PV
en
er
g
y
s
y
s
tem
s
(
PVES)
,
wh
er
e
th
ey
ca
n
h
an
d
le
v
ar
iab
le
s
p
ee
d
s
,
elim
in
ate
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
,
an
d
m
ax
im
ize
en
er
g
y
ex
tr
a
ctio
n
.
Mu
ltil
ev
el
in
v
er
ter
s
ar
e
ch
ar
ac
ter
ized
b
y
lo
wer
p
o
wer
lo
s
s
es d
u
r
in
g
th
e
s
witch
in
g
p
r
o
ce
s
s
[
2
2
]
,
[
2
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
41
,
No
.
2
,
Feb
r
u
a
r
y
20
2
6
:
4
5
6
-
4
6
9
460
3
.
1
.
Descript
io
n o
f
t
he
NP
C
t
o
po
lo
g
y
Th
e
NPC
to
p
o
lo
g
y
is
a
f
am
ily
o
f
m
u
ltil
ev
el
c
o
n
v
e
r
ter
s
ch
ar
ac
ter
ized
b
y
t
h
e
u
s
e
o
f
clam
p
i
n
g
d
io
d
es
th
at
d
iv
id
e
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
p
o
wer
s
witch
es.
T
h
e
s
tr
u
ct
u
r
e
o
f
t
h
e
NPC
to
p
o
l
o
g
y
is
co
m
p
o
s
ed
o
f
m
u
ltip
le
s
tag
es
o
f
s
wi
tch
es
an
d
clam
p
in
g
d
io
d
es,
ar
r
an
g
ed
to
d
iv
id
e
th
e
in
p
u
t
v
o
ltag
e
in
to
m
u
lti
p
le
o
u
tp
u
t
v
o
ltag
e
lev
els.
A
ty
p
ical
th
r
ee
-
lev
el
NPC
in
v
er
ter
,
f
o
r
e
x
am
p
le,
in
clu
d
es
two
DC
v
o
ltag
e
s
o
u
r
ce
s
,
f
o
u
r
s
witch
es
(
I
GB
T
s
)
,
an
d
two
clam
p
in
g
d
i
o
d
es p
er
p
h
ase.
T
h
e
NPC
co
n
f
ig
u
r
atio
n
allo
w
s
f
o
r
ev
en
d
is
tr
ib
u
tio
n
o
f
v
o
ltag
es
an
d
cu
r
r
en
ts
b
etwe
en
t
h
e
v
ar
io
u
s
s
witch
es
an
d
d
io
d
es
,
r
ed
u
cin
g
s
tr
ess
o
n
ea
ch
co
m
p
o
n
e
n
t.
T
h
is
n
o
t
o
n
ly
im
p
r
o
v
es
co
m
p
o
n
en
t
r
eliab
ilit
y
an
d
life
s
p
an
b
u
t
also
o
v
er
all
s
y
s
t
em
ef
f
icien
cy
.
T
h
e
ab
ilit
y
to
cr
ea
te
m
u
ltip
le
in
ter
m
ed
iate
v
o
ltag
e
lev
els
also
h
elp
s
to
r
ed
u
ce
h
ar
m
o
n
ics in
t
h
e
o
u
tp
u
t w
av
ef
o
r
m
,
th
e
r
eb
y
i
m
p
r
o
v
i
n
g
p
o
wer
q
u
ality
.
3
.
1
.
1
.
Str
uct
ure
o
f
t
he
t
hree
-
l
ev
el
NP
C
Fo
r
a
th
r
ee
-
lev
el
NPC
to
p
o
lo
g
y
,
th
e
t
y
p
ical
s
tr
u
ctu
r
e
u
s
es
two
DC
v
o
ltag
e
s
o
u
r
ce
s
(
o
r
a
DC
b
u
s
o
f
ca
p
ac
ito
r
s
)
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
is
o
b
tai
n
ed
b
y
co
m
b
in
in
g
th
ese
s
o
u
r
ce
s
in
a
co
n
tr
o
lled
m
a
n
n
er
u
s
in
g
th
e
f
o
u
r
(
4
)
I
GB
T
s
p
r
esen
t
in
th
e
th
r
ee
-
lev
el
s
tr
u
ctu
r
e.
T
h
e
d
io
d
es
w
ill
b
e
co
n
n
ec
ted
b
etwe
en
two
s
u
cc
ess
iv
e
s
o
u
r
ce
s
,
allo
win
g
th
e
d
if
f
er
en
t
in
ter
m
ed
iate
lev
els
to
b
e
r
ep
r
o
d
u
ce
d
.
Fig
u
r
e
5
s
h
o
ws
th
e
t
o
p
o
lo
g
y
o
f
a
th
r
ee
-
p
h
ase,
th
r
ee
-
lev
el
NPC
.
Fig
u
r
e
5
.
T
o
p
o
lo
g
y
o
f
th
r
e
e
-
p
h
ase
th
r
ee
-
lev
el
NPC
3
.
1
.
2
.
Str
uct
ure
o
f
t
he
f
i
v
e
-
le
v
el
NP
C
Fo
r
a
f
iv
e
-
lev
el
NPC
to
p
o
lo
g
y
,
th
e
ty
p
ical
s
tr
u
ctu
r
e
u
s
es
f
o
u
r
DC
v
o
ltag
e
s
o
u
r
ce
s
(
o
r
a
DC
b
u
s
o
f
ca
p
ac
ito
r
s
)
.
T
h
e
o
u
tp
u
t v
o
ltag
e
is
o
b
tain
ed
b
y
co
m
b
in
in
g
th
ese
s
o
u
r
ce
s
in
a
c
o
n
tr
o
lled
m
a
n
n
er
u
s
in
g
th
e
eig
h
t
(
8
)
I
GB
T
s
p
r
esen
t
in
th
e
f
iv
e
-
lev
el
s
tr
u
ctu
r
e.
T
h
e
d
io
d
es
wi
ll
b
e
c
o
n
n
ec
te
d
b
etwe
en
two
s
u
cc
ess
iv
e
s
o
u
r
ce
s
,
allo
win
g
th
e
d
i
f
f
er
en
t
in
ter
m
ed
iate
le
v
els
to
b
e
r
ep
r
o
d
u
ce
d
.
Fig
u
r
e
6
s
h
o
ws
th
e
t
o
p
o
l
o
g
y
o
f
a
th
r
ee
-
p
h
ase
f
iv
e
-
lev
el
NPC
.
Fig
u
r
e
6
.
T
o
p
o
lo
g
y
o
f
th
r
e
e
-
p
h
ase
f
iv
e
lev
el
NPC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
C
o
n
tr
o
l o
f m
u
lti
-
leve
l NPC
in
ve
r
ters
in
P
V
/g
r
id
s
y
s
tems u
s
i
n
g
A
DR
C
a
n
d
MADR
C
(
Gh
erici Din
a
r
)
461
4.
G
RID
SI
D
E
CO
NV
E
R
T
E
R
M
O
DE
L
I
NG
E
lectr
ic
p
o
wer
g
en
er
atio
n
s
y
s
tem
s
with
r
en
ewa
b
le
s
o
u
r
ce
s
o
f
en
er
g
y
o
f
all
k
in
d
s
,
s
u
c
h
as
win
d
en
er
g
y
,
s
ea
wav
e
en
er
g
y
,
s
o
l
ar
en
er
g
y
ce
lls
,
an
d
o
th
er
v
a
r
io
u
s
s
o
u
r
ce
s
,
d
ep
e
n
d
o
n
th
e
g
r
id
-
s
id
e
co
n
v
er
ter
(
GSC
)
,
wh
ich
p
er
m
its
cu
r
r
en
t
f
lo
w
f
r
o
m
an
d
t
o
th
e
g
r
id
,
t
h
at
m
ain
co
n
v
er
tin
g
DC
-
lin
k
v
o
ltag
e
Vd
c
to
AC
v
o
ltag
e,
o
r
v
ice
v
e
r
s
a
[
2
4
]
.
Fi
g
u
r
e
7
d
e
p
icts
th
e
GSC
;
it
co
n
s
is
ts
o
f
1
2
elec
tr
o
n
ic
s
witch
es
(
S1
1
…S3
4
)
,
a
n
d
ea
ch
s
witch
is
a
p
h
ase.
A
tr
a
n
s
is
to
r
an
d
a
d
io
d
e
ar
e
co
n
n
ec
ted
in
p
ar
allel,
an
d
th
ese
twelv
e
s
witch
es
ar
e
d
is
tr
ib
u
ted
o
v
er
th
r
ee
co
lu
m
n
s
,
an
d
th
e
t
h
r
ee
co
lu
m
n
s
ar
e
c
o
n
n
ec
ted
to
th
e
g
r
id
th
r
o
u
g
h
t
h
r
ee
id
e
n
tical
co
ils
with
L
filter
in
d
u
ctan
ce
a
n
d
R
filter
r
esis
tan
ce
.
Fig
u
r
e
7
.
Stru
ctu
r
e
o
f
th
e
g
r
id
s
id
e
co
n
v
er
ter
A
GSC
ca
n
b
e
r
ep
r
esen
ted
in
a
d
-
q
r
o
tatin
g
c
o
o
r
d
i
n
ate
as
f
o
llo
ws [
2
5
]
,
[
2
6
]
:
=
1
(
−
+
+
−
)
(
10
)
=
1
(
−
−
+
−
)
(
11
)
T
h
e
DC
lin
k
v
o
ltag
e
r
elatio
n
s
h
ip
is
g
iv
en
as
f
o
llo
ws [
2
5
]
,
[
2
6
]
:
=
1
(
−
+
−
)
(
12
)
5.
L
I
N
E
AR
AD
RC
CO
NT
RO
L
Han
[
2
7
]
p
r
o
p
o
s
ed
t
h
e
ef
f
ec
tiv
e
ADRC
tech
n
iq
u
e
in
2
0
0
9
[
2
8
]
.
T
h
e
tr
ac
k
in
g
d
if
f
er
en
ti
ato
r
(
T
D)
,
E
SO,
an
d
n
o
n
lin
ea
r
s
tate
er
r
o
r
f
ee
d
b
ac
k
(
NL
SEF)
ar
e
th
e
t
h
r
ee
p
r
im
ar
y
co
m
p
o
n
e
n
ts
o
f
t
h
e
ADRC
co
n
tr
o
ller
[
2
4
]
.
Str
u
ctu
r
e
o
f
th
e
ADRC
co
n
tr
o
ller
is
illu
s
tr
ated
in
Fig
u
r
e
8
.
Fig
u
r
e
8
.
Stru
ctu
r
e
o
f
th
e
AD
R
C
co
n
tr
o
ller
A
lo
t
o
f
s
ettin
g
s
in
th
e
ADRC
co
n
tr
o
ller
n
ee
d
to
b
e
ch
a
n
g
e
d
in
p
r
ac
tice,
an
d
it’s
d
if
f
icu
lt
to
ch
a
n
g
e
th
ese
p
ar
am
eter
s
[
2
4
]
,
[
2
9
]
.
I
n
lig
h
t
o
f
th
is
,
a
lin
ea
r
ADR
C
d
esig
n
m
eth
o
d
is
r
ec
o
m
m
en
d
ed
an
d
u
s
ed
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
41
,
No
.
2
,
Feb
r
u
a
r
y
20
2
6
:
4
5
6
-
4
6
9
462
co
n
tr
o
l
th
e
DC
lin
k
v
o
ltag
e
in
th
e
g
r
i
d
-
s
id
e
co
n
v
er
t
er
,
co
n
tr
o
l
th
e
s
p
ee
d
o
f
t
h
e
PMSG,
an
d
r
eg
u
late
th
e
in
p
u
t
cu
r
r
en
t
o
f
t
h
e
b
o
o
s
t
co
n
v
er
te
r
in
o
r
d
er
to
d
ec
r
ea
s
e
th
e
m
o
d
el
co
m
p
le
x
ity
an
d
th
e
co
n
tr
o
ller
co
m
p
u
tatio
n
al
r
eq
u
ir
em
e
n
ts
.
A
p
r
o
p
o
r
tio
n
al
co
n
t
r
o
ller
k
p
an
d
an
E
SO
m
ak
e
u
p
th
e
L
A
DR
C
.
E
x
ter
n
al
d
is
tu
r
b
an
c
es
an
d
s
y
s
tem
u
n
ce
r
tain
ty
ar
e
s
ee
n
as
a
s
in
g
le,
g
en
er
alize
d
d
is
tu
r
b
a
n
ce
.
T
h
e
g
en
e
r
alize
d
d
is
tu
r
b
an
ce
an
d
s
y
s
tem
s
tates
ar
e
esti
m
ated
u
s
in
g
th
e
E
SO.
T
h
e
tr
ac
k
in
g
er
r
o
r
b
etwe
en
th
e
s
y
s
tem
'
s
o
u
tp
u
t
an
d
th
e
r
ef
er
e
n
ce
s
ig
n
al
is
d
r
iv
en
to
ze
r
o
b
y
th
e
p
r
o
p
o
r
tio
n
a
l c
o
n
tr
o
ller
[
2
5
]
,
[
3
0
]
.
A
f
ir
s
t
-
o
r
d
er
s
y
s
tem
d
e
f
in
ed
b
y
(
9
)
is
o
n
e
with
a
s
in
g
le
in
p
u
t
an
d
a
s
in
g
le
o
u
tp
u
t
y
.
(
)
=
(
,
,
)
+
0
(
)
(
1
)
W
h
er
e
b
0
is
th
e
k
n
o
wn
p
o
r
ti
o
n
o
f
th
e
s
y
s
tem
an
d
f(
y,
d
,
t)
r
ep
r
esen
ts
th
e
d
y
n
am
ic
m
o
d
el
an
d
an
y
s
y
s
tem
d
is
tu
r
b
an
ce
s
(
in
te
r
n
al
a
n
d
ex
te
r
n
al)
.
T
h
e
s
y
s
tem
d
escr
ib
ed
in
(
9
)
is
g
iv
e
n
a
r
e
p
r
esen
tatio
n
i
n
s
tate
v
ar
ia
b
les
as
s
h
o
wn
in
(
1
0
)
-
(
1
1
)
.
1
=
2
+
0
(
)
(
14
)
2
=
(
15
)
T
h
e
f
ir
s
t
-
o
r
d
er
lin
ea
r
ADRC
,
in
clu
d
in
g
th
e
E
SO,
is
g
iv
en
as:
1
=
2
+
0
(
)
−
1
(
16
)
2
=
−
2
(
17
)
=
1
−
(
18
)
(
)
=
−
0
(
19
)
0
=
(
−
1
)
(
20
)
W
h
er
e
1
is
th
e
esti
m
ated
o
u
tp
u
t
.
[
1
2
]
=
[
2
0
0
2
]
i
t
is
th
e
o
b
s
er
v
er
g
ain
v
ec
to
r
.
0
Den
o
tes
th
e
o
b
s
er
v
er
'
s
cu
t
-
o
f
f
p
u
ls
e
;
it
s
h
o
u
ld
b
e
em
p
h
asized
th
at
wh
ile
a
b
ig
p
u
ls
e
allo
ws
f
o
r
a
d
ec
en
t
ass
ess
m
en
t
o
f
th
e
s
tates,
it
also
r
u
n
s
th
e
d
an
g
er
o
f
m
ak
in
g
th
e
s
y
s
tem
m
o
r
e
s
en
s
itiv
e
to
n
o
is
e.
I
t
s
h
o
u
ld
b
e
o
b
s
er
v
ed
th
at
a
lar
g
e
p
u
ls
atio
n
allo
ws
f
o
r
th
e
p
o
s
s
ib
ilit
y
o
f
th
e
esti
m
ated
v
ar
iab
les
1
→
y
2
→
b
ein
g
u
s
ed
to
o
f
f
s
et
all
d
is
tu
r
b
an
ce
s
b
y
u
s
in
g
th
e
c
o
n
t
r
o
l la
w,
as sh
o
wn
in
(
1
6
)
.
T
h
e
co
n
tr
o
ller
g
ai
n
p
is
d
en
o
ted
b
y
,
wh
ich
is
th
e
clo
s
ed
-
lo
o
p
n
atu
r
al
f
r
eq
u
en
c
y
,
an
d
is
th
e
r
ef
er
en
ce
s
ig
n
al.
C
o
m
p
ar
ed
t
o
th
e
d
y
n
am
ics
o
f
th
e
c
o
n
tr
o
l
ler
,
th
e
o
b
s
er
v
er
'
s
d
y
n
am
ics
m
u
s
t
b
e
s
wif
t.
As
a
r
esu
lt,
th
e
o
b
s
er
v
er
'
s
p
o
les
ar
e
p
o
s
itio
n
ed
to
th
e
lef
t
o
f
t
h
e
clo
s
ed
-
lo
o
p
s
y
s
tem
'
s
p
o
les.
T
y
p
ically
,
0
is
s
elec
ted
s
o
th
at
0
=
(
3
-
1
0
)
[
3
0
]
.
6.
VO
CO
NT
RO
L
O
F
G
SC
T
h
e
aim
o
f
th
e
c
o
n
tr
o
l
s
y
s
tem
o
f
GSC
is
to
r
eg
u
late
th
e
DC
lin
k
v
o
ltag
e
at
V
dc
-
ref
in
th
e
o
u
ter
lo
o
p
u
s
in
g
ADRC
tech
n
o
lo
g
y
an
d
r
eg
u
late
th
e
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
wer
in
t
h
e
in
n
er
l
o
o
p
u
s
in
g
a
PI
co
n
tr
o
ller
,
wh
er
e
th
e
r
ef
er
e
n
ce
v
alu
e
o
f
t
h
e
r
ea
ctiv
e
p
o
wer
i
s
eq
u
al
to
ze
r
o
.
Ass
u
m
in
g
th
at
th
e
co
o
r
d
in
ate
ax
es
(
d
,
q
)
a
r
e
o
r
ien
tated
s
o
th
at
th
e
d
-
a
x
is
a
p
p
lies
to
th
e
g
r
id
v
o
ltag
e
v
ec
t
o
r
V
s
,
w
h
ich
m
ea
n
s
V
q
=0
,
t
h
e
n
th
e
f
o
llo
win
g
two
r
elatio
n
s
ca
n
b
e
o
b
tain
ed
f
o
r
t
h
e
elec
tr
ical
p
o
wer
p
ass
ed
b
y
th
e
GSC
s
:
=
1
.
5
=
−
−
(
21
)
=
−
1
.
5
(
22
)
Fo
r
a
u
n
it
p
o
wer
f
ac
to
r
,
th
e
r
e
f
er
en
ce
cu
r
r
en
t
i
q
is
s
et
to
ze
r
o
,
th
u
s
th
e
GSC
co
n
tr
o
l
s
y
s
tem
h
as
two
r
eg
u
latin
g
ax
es:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
C
o
n
tr
o
l o
f m
u
lti
-
leve
l NPC
in
ve
r
ters
in
P
V
/g
r
id
s
y
s
tems u
s
i
n
g
A
DR
C
a
n
d
MADR
C
(
Gh
erici Din
a
r
)
463
i)
q
ax
is
: th
e
cu
r
r
e
n
t i
q
is
r
eg
u
lat
ed
at
ze
r
o
.
ii)
d
ax
is
:
i
t
i
n
clu
d
es
two
r
eg
u
latin
g
lo
o
p
s
,
t
h
e
f
i
r
s
t
is
an
ex
ter
n
al
r
eg
u
latin
g
lo
o
p
th
r
o
u
g
h
wh
ich
th
e
DC
lin
k
v
o
ltag
e
is
r
eg
u
lated
ac
co
r
d
in
g
to
th
e
r
ef
er
en
ce
v
alu
e
,
an
d
th
e
s
ec
o
n
d
is
an
in
ter
n
al
r
eg
u
latin
g
lo
o
p
th
r
o
u
g
h
wh
ich
th
e
cu
r
r
e
n
t
i
d
is
r
e
g
u
la
ted
ac
co
r
d
in
g
to
th
e
r
ef
e
r
en
c
e
v
alu
e
d
eter
m
in
e
d
b
y
th
e
v
o
ltag
e
r
eg
u
latin
g
lo
o
p
.
7.
ADR
CO
NT
RO
L
O
F
DC
-
L
I
NK
VO
L
T
AG
E
T
h
e
im
p
lem
en
tatio
n
o
f
t
h
e
A
DR
co
n
tr
o
l is d
etailed
in
Fig
u
r
e
9
:
Fig
u
r
e
9
.
Gr
id
s
id
e
co
n
v
er
ter
c
o
n
tr
o
l b
y
ADRC
T
o
co
n
tr
o
l th
e
DC
-
lin
k
v
o
ltag
e,
an
d
if
we
c
o
n
s
id
er
th
at
i
q
is
s
et
to
ze
r
o
,
th
en
we
ca
n
r
ewr
it
e
(
8
)
as f
o
ll
o
ws:
=
−
1
+
(
23
)
is
r
elate
d
to
th
e
tr
an
s
f
o
r
m
r
ati
o
o
f
GSC
.
I
n
(
1
9
)
ca
n
b
e
r
ewr
itten
as sh
o
wn
:
=
(
.
)
+
0
(
24
)
T
h
e
d
c
-
lin
k
v
o
ltag
e
ADR
co
n
tr
o
ller
is
d
esig
n
ed
by
(
2
2
)
-
(
2
8
)
,
as sh
o
wn
:
1
=
(
.
)
+
−
1
1
(
25
)
(
.
)
=
−
2
1
(
26
)
1
=
1
−
(
27
)
=
−
(
.
)
(
28
)
=
(
−
−
1
)
(
29
)
W
h
er
e:
(
.
)
=
(
1
,
)
(
30
)
0
=
2
(
31
)
=
−
(
32
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
41
,
No
.
2
,
Feb
r
u
a
r
y
20
2
6
:
4
5
6
-
4
6
9
464
8.
M
ADR
CO
N
T
RO
L
O
F
DC
-
L
I
NK
VO
L
T
AG
E
A
M
ADR
C
is
a
co
n
tr
o
l
s
tr
ateg
y
th
at
b
u
ild
s
u
p
o
n
th
e
s
tan
d
ar
d
ADRC
f
r
am
ewo
r
k
t
o
im
p
r
o
v
e
p
er
f
o
r
m
an
ce
an
d
ad
d
r
ess
s
p
ec
if
ic
ch
allen
g
es.
I
t
o
f
ten
in
v
o
lv
es
m
o
d
if
icatio
n
s
to
th
e
E
S
O
o
r
th
e
co
n
tr
o
l
law
its
elf
,
aim
in
g
f
o
r
b
etter
d
is
tu
r
b
an
ce
r
ejec
tio
n
,
t
r
ac
k
in
g
ac
cu
r
ac
y
,
o
r
r
o
b
u
s
tn
ess
to
u
n
ce
r
tai
n
ties
.
T
h
e
g
r
id
-
s
id
e
co
n
v
er
ter
co
n
t
r
o
l
b
y
MA
DR
C
is
s
im
ilar
to
Fig
u
r
e
9
,
wh
er
e
th
e
ADRC
co
n
tr
o
l
h
as
b
ee
n
c
h
an
g
ed
to
MA
R
DC
co
n
tr
o
l.
Neg
lectin
g
th
e
ex
ter
n
al
d
is
tu
r
b
an
ce
in
th
e
r
elatio
n
(
1
9
)
,
we
f
in
d
:
=
2
(
33
)
Su
p
p
o
s
e
th
e
f
o
llo
win
g
er
r
o
r
r
e
latio
n
s
h
ip
:
2
=
−
(
34
)
B
y
d
er
iv
atio
n
,
a
f
ter
s
u
b
s
titu
tin
g
th
e
r
elatio
n
(
2
9
)
,
we
f
in
d
:
2
̇
=
−
2
(
35
)
Ass
u
m
in
g
a
L
y
ap
u
n
o
v
f
u
n
ctio
n
:
=
0
.
5
2
2
(
36
)
B
y
d
er
iv
in
g
t
h
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
an
d
s
u
b
s
titu
tin
g
th
e
r
elat
io
n
(
3
1
)
,
we
f
i
n
d
:
̇
=
−
2
2
(
37
)
T
h
e
co
n
tr
o
l la
w
i
d
ca
n
b
e
ch
o
s
en
as f
o
llo
ws:
=
2
2
(
38
)
C
o
m
p
en
s
atio
n
in
th
e
r
elatio
n
s
h
ip
(
3
3
)
we
f
in
d
:
̇
=
−
2
2
(
39
)
T
h
er
ef
o
r
e,
a
p
o
s
itiv
e
v
alu
e
o
f
k
m
u
s
t b
e
ch
o
s
en
t
o
en
s
u
r
e
t
h
e
s
tab
ilit
y
o
f
th
e
s
y
s
tem
.
T
h
u
s
,
b
ased
o
n
th
e
r
elatio
n
s
(
2
9
)
-
(
3
5
)
,
th
e
f
o
llo
win
g
d
i
f
f
er
en
tial
r
elatio
n
ca
n
b
e
wr
itten
ex
p
r
ess
in
g
th
e
tr
an
s
f
er
f
u
n
ctio
n
b
etwe
en
V
r
ef
an
d
V
dc
:
=
−
+
(
40
)
R
ed
esig
n
in
g
th
e
ADRC
co
n
tr
o
ller
to
r
eg
u
late
DC
-
lin
k
v
o
lta
g
e
b
ased
o
n
(
3
6
)
will b
e
as f
o
l
lo
ws:
1
=
(
.
)
+
−
1
1
(
41
)
(
.
)
=
−
2
1
(
42
)
1
=
1
−
(
43
)
=
−
(
.
)
(
44
)
=
(
−
−
1
)
(
45
)
Wh
e
re
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
C
o
n
tr
o
l o
f m
u
lti
-
leve
l NPC
in
ve
r
ters
in
P
V
/g
r
id
s
y
s
tems u
s
i
n
g
A
DR
C
a
n
d
MADR
C
(
Gh
erici Din
a
r
)
465
(
.
)
=
(
−
,
1
)
(
46
)
=
(
47
)
=
(
48
)
9.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
T
h
e
s
im
u
latio
n
was
ex
ac
ted
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
s
o
f
twar
e.
Simu
latio
n
s
wer
e
co
n
d
u
cted
f
o
r
u
s
in
g
th
e
th
r
ee
-
a
n
d
f
iv
e
-
lev
el
ty
p
e
(
NPC
)
in
v
er
ter
in
th
e
P
V/g
r
id
.
I
n
th
is
s
ec
tio
n
we
p
r
e
s
en
t
th
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
p
r
o
p
o
s
ed
co
n
t
r
o
l
s
tr
ateg
y
f
o
r
a
PV
s
y
s
tem
co
n
n
ec
ted
to
th
r
ee
-
p
h
ase
u
tili
ty
g
r
id
(
3
8
0
v
/5
0
Hz)
.
Simu
latio
n
wer
e
co
n
d
u
cted
f
o
r
u
s
in
g
th
e
th
r
ee
-
an
d
f
iv
e
-
l
e
v
e
l
(
NPC
)
in
v
er
ter
s
o
f
p
r
o
p
o
s
ed
co
n
tr
o
l
ADRC
an
d
MA
DR
C
.
T
h
e
DC
lin
k
v
o
ltag
e
was m
ain
tain
ed
to
its
r
ef
er
en
ce
as it
is
s
h
o
wn
in
Fig
u
r
e
1
0
,
wh
ich
illu
s
tr
ates th
e
r
esp
o
n
s
e
o
f
d
if
f
er
en
t
co
n
tr
o
l
s
y
s
tem
s
in
r
eg
u
latin
g
th
e
DC
lin
k
v
o
ltag
e.
Fro
m
th
is
f
ig
u
r
e,
a
c
o
m
p
a
r
is
o
n
f
o
r
Vd
c
b
etwe
en
u
s
in
g
a
th
r
ee
l
ev
el
(
NPC
)
co
n
v
er
ter
a
n
d
a
f
iv
e
lev
el
(
NPC
)
co
n
v
e
r
ter
is
r
ev
iewe
d
with
th
e
ap
p
lied
o
f
two
d
if
f
e
r
en
t c
o
n
tr
o
l te
ch
n
iq
u
es AD
R
C
an
d
MA
DR
C
co
n
tr
o
l.
T
h
e
DC
-
lin
k
v
o
ltag
e
is
p
lo
tte
d
o
v
e
r
tim
e,
with
t
h
e
r
ef
e
r
en
c
e
v
o
ltag
e
s
et
at
6
2
5
V.
All
f
o
u
r
s
y
s
tem
s
s
tar
t
at
th
e
s
am
e
in
itial
v
o
ltag
e
an
d
attem
p
t
to
r
ea
ch
an
d
m
a
in
tain
th
e
r
ef
er
e
n
ce
v
alu
e.
T
h
e
f
iv
e
-
le
v
el
in
v
er
ter
co
n
tr
o
lled
u
s
in
g
MA
DR
C
ac
h
iev
es
th
e
r
ef
e
r
en
ce
v
o
ltag
e
r
ap
id
ly
(
6
2
5
V
with
in
0
.
0
2
t
o
0
.
2
s
ec
o
n
d
s
)
an
d
ex
h
ib
its
m
in
im
al
o
s
cillatio
n
s
,
r
ef
lectin
g
its
s
u
p
er
io
r
s
tab
ilit
y
.
T
h
e
th
r
ee
-
lev
el
in
v
e
r
ter
co
n
tr
o
lled
u
s
in
g
MA
DR
C
s
h
o
ws
th
e
s
ec
o
n
d
-
b
est
p
er
f
o
r
m
an
ce
,
with
a
s
lig
h
tly
s
lo
wer
r
esp
o
n
s
e
tim
e
an
d
m
ar
g
in
ally
m
o
r
e
o
s
cillatio
n
th
an
th
e
ADRC
.
T
h
e
th
r
ee
-
lev
el
in
v
er
te
r
co
n
tr
o
lled
u
s
in
g
ADRC
ex
h
ib
its
th
e
s
lo
west r
esp
o
n
s
e
an
d
th
e
m
o
s
t
s
ig
n
if
ican
t
o
s
cillatio
n
s
ar
o
u
n
d
th
e
r
ef
e
r
en
ce
v
o
ltag
e.
No
tab
ly
,
all
s
y
s
tem
s
ex
p
er
ien
ce
s
o
m
e
d
is
tu
r
b
an
ce
s
,
lik
el
y
c
o
r
r
esp
o
n
d
in
g
to
ch
an
g
es
in
s
o
lar
r
a
d
ia
tio
n
,
b
u
t
th
e
MA
DR
C
co
n
tr
o
l
led
s
h
o
ws
s
u
p
er
io
r
ab
ilit
y
in
q
u
ick
ly
o
v
er
c
o
m
in
g
th
ese
d
is
tu
r
b
an
ce
s
a
n
d
r
et
u
r
n
in
g
to
th
e
r
e
f
er
en
ce
v
o
ltag
e
.
T
h
is
g
r
ap
h
clea
r
ly
illu
s
tr
ates
th
e
en
h
an
ce
d
d
y
n
a
m
ic
p
er
f
o
r
m
an
ce
a
n
d
d
is
tu
r
b
an
ce
r
ejec
tio
n
ca
p
ab
ilit
ies
o
f
MA
DR
C
co
n
tr
o
l
s
tr
ateg
ies,
p
ar
ticu
lar
ly
t
h
e
f
iv
e
lev
els
u
s
in
g
MA
DR
C
co
n
tr
o
l,
in
m
ain
tain
in
g
a
s
tab
le
DC
-
lin
k
v
o
ltag
e
u
n
d
e
r
v
ar
y
in
g
co
n
d
itio
n
s
.
T
h
e
ac
tiv
e
p
o
wer
tr
an
s
m
itted
to
th
e
g
r
id
u
n
d
er
d
if
f
er
e
n
t
co
n
tr
o
l
s
y
s
tem
s
is
illu
s
tr
ated
in
Fig
u
r
e
1
1
.
T
h
e
ch
ar
ac
ter
is
tic
s
h
o
ws
f
o
u
r
d
is
tin
ct
cu
r
v
es
r
ep
r
esen
tin
g
th
e
p
er
f
o
r
m
a
n
ce
o
f
v
a
r
io
u
s
co
n
t
r
o
l
s
tr
ateg
ies.
T
h
e
b
lu
e
cu
r
v
e
c
o
r
r
esp
o
n
d
s
to
th
e
th
r
ee
-
lev
el
(
NPC
)
in
v
er
ter
with
ADRC
co
n
tr
o
ller
,
th
e
r
ed
cu
r
v
e
co
r
r
esp
o
n
d
s
to
th
e
f
iv
e
-
lev
el
(
NPC
)
in
v
er
ter
with
ADR
C
co
n
tr
o
ller
,
th
e
y
ello
w
cu
r
v
e
co
r
r
esp
o
n
d
s
to
th
e
th
r
ee
-
lev
el
(
NPC
)
in
v
er
ter
with
MA
DR
C
co
n
tr
o
ller
,
an
d
th
e
v
io
let
cu
r
v
e
c
o
r
r
esp
o
n
d
s
to
th
e
f
iv
e
-
lev
el
(
NPC
)
in
v
er
ter
with
MA
DR
C
co
n
tr
o
ller
.
T
h
is
is
th
e
f
o
u
r
t
h
co
n
t
r
o
l
s
y
s
tem
th
at
a
ch
iev
es
th
e
h
ig
h
est
ac
tiv
e
p
o
wer
tr
an
s
m
is
s
io
n
to
th
e
g
r
id
,
T
ab
le
1
f
o
r
t
h
e
p
ar
am
eter
o
f
th
e
ADRC
an
d
MA
DR
C
co
n
tr
o
ller
.
Fig
u
r
e
1
0
.
C
o
n
tr
o
l sy
s
tem
s
r
esp
o
n
s
e
to
r
e
g
u
late
th
e
DC
-
lin
k
v
o
ltag
e
T
ab
le
1
.
T
h
e
p
ar
am
ete
r
o
f
th
e
ADR
C
an
d
MA
DR
C
co
n
tr
o
ller
P
a
r
a
me
t
e
r
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